In this thesis, we discussed the application of the single-(Dirac) particle model to understand some physical behaviors of the graphene related systems (including also bilayer graphene, etc.) At first, we derive the low-energy Hamiltonians by the minimal tight-binding model that only includes hopping between nearest neighbor carbon atoms. We then discuss in detail the topics that can be treated by supersymmetry quantum mechanics (SUSY QM), including the low-energy eigenvalues and eigenfunctions of the graphene related systems in the magnetic field and the application to understand the anomalous quantum Hall effects observed in these systems. Finally, by making use of shape invariant potentials approach of SUSY QM, we discuss the bound-state problem of the Dirac particle scattered by a single impurity with the long-range attractive Coulomb potential and its application to the graphene system.